Topic 2. Continuity of functions of one variable.
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Limit of a function in a point. One-sided limits. Continuity. The intermediate value theorem. Bolzano's theorem. The bisection method.
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Topic 4. Derivatives of functions of one variable and applications of the derivative. |
Derivatives of a function at a point. Derivative function, successive derivatives, properties. Chain rule. Implicit differentiation. Derivative of inverse functions. Maxima and minima. Mean value theorem. L'Hopital's rule. Local study of the graph of a function. Taylor polynomials. Newton's method. |
Topic 6. Applications of the differential calculus.
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Extreme values. Extreme values with equality constraints. Newton's method. |